Oil Volatility Risk. Lin Gao, Steffen Hitzemann, Ivan Shaliastovich, and Lai Xu. Preliminary Version. June Abstract

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1 Oil Volatility Risk Lin Gao, Steffen Hitzemann, Ivan Shaliastovich, and Lai Xu Preliminary Version June 216 Abstract In the data, an increase in oil price volatility dampens current and future output, investment, employment, and consumption, controlling for the market volatility and other business cycle variables. High oil uncertainty negatively affects equity prices, with a much more pronounced impact in durable industries. We develop a two-sector production model to explain the novel evidence in the data. In the model, oil is an essential input for production and can be stored. At times of high oil supply volatility, firms optimally decide to stock up oil, rather than to invest in physical capital. As a result, investment, production, and consumption go down, while oil inventories go up. These mechanisms are directly supported in the data. Lin Gao (lin.gao@uni.lu) is at the University of Luxembourg. Steffen Hitzemann (hitzemann.6@osu.edu) is at the Ohio State University. Ivan Shaliastovich (ishal@wharton.upenn.edu) is at the Wharton School, University of Pennsylvania. Lai Xu (lxu1@syr.edu) is at Syracuse University. We thank John Elder, Leonid Kogan, Amir Yaron, as well as participants of the 216 Western Finance Association conference and the 216 North American Summer Meeting of the Econometric Society for valuable discussions and helpful comments and suggestions. 1

2 1 Introduction The recent literature has documented that aggregate uncertainty fluctuations have a significant adverse effect on the macroeconomy and on asset markets. In the data, an increase in aggregate macroeconomic uncertainty is typically associated with lower economic growth in the future and lower equity valuations. 1 In this paper, we consider uncertainty emanating from an economically important sector that involves production of oil. We show that oil uncertainty fluctuations have a separate and significant impact on economic growth and asset prices which is not captured by aggregate macroeconomic and financial volatilities or other business cycle variables. An increase in oil uncertainty dampens output, investment, and consumption, and has a negative impact on asset prices in industries that are sensitive to oil as an input factor (such as Durables and Autos), while the exposure of industries related to the production of oil and oil products is positive. We develop a two-sector production model which features a trade-off between physical capital accumulation and storage of oil to explain the novel evidence in the data. Our benchmark empirical evidence is based on implied volatility measures constructed from option price data in oil and equity markets. Using regression analysis, we find that an increase in oil volatility predicts a decline in current and future growth of macroeconomic variables, such as consumption, output, investment, employment, and aggregate dividends, one to four quarters ahead, controlling for the current growth rates in the corresponding variables as well as for oil returns and the market variance. These results, based on market price data to measure uncertainties, corroborate and extend the findings of Elder and Serletis (21) who find a statistically significant negative impact of oil volatility on several measures 1 Ramey and Ramey (1995), Fernandez-Villaverde, Guerrón-Quintana, Rubio-Ramirez, and Uribe (211), Basu and Bundick (212), Bansal, Kiku, Shaliastovich, and Yaron (214), Bloom (214), Gilchrist, Sim, and Zakrajsek (214) show a negative relation between real economic growth and macroeconomic uncertainty, while Bansal and Yaron (24), Bansal, Khatchatrian, and Yaron (25), Lettau, Ludvigson, and Wachter (28) discuss the link between uncertainty and financial markets. 2

3 of aggregate growth, using a bivariate GARCH-in-mean approach. Economically, the impact of oil volatility is quite large. Following a one standard deviation increase in oil variance, consumption growth declines by about.3%, annualized, and future output and investment drop by.66% and 2.75%, respectively, using a conservative shock orthogonalization in which equity variance leads oil variance. An increase in oil variance further predicts a decline in oil consumption and an increase in oil inventories: oil inventories increase by.5% while oil consumption declines by about.6% one quarter after a one-standard deviation shock to oil uncertainty. At the same time, aggregate total factor productivity (TFP) and production of oil do not seem to be significantly related to movements in oil volatility, which suggests that the response of macroeconomic variables, such as consumption and output, to oil volatility is not mechanically inherited from the dynamics of productivity. We further show that the market equity price drops at times of high oil uncertainty. Oil prices themselves only have a weak relation to oil uncertainty; in fact, the correlation is positive outside the Financial crisis. This evidence is supported by the cross-section of equity returns which suggests that industries which are likely to use oil as an essential input, such as Durables and primarily Autos, have a large negative exposure to oil uncertainty. On the other hand, industries which are involved in the production of oil and oil-related products (Energy) have the largest positive exposure to oil volatility. Consistent with the hypothesis in Bernanke (1983) that the consumption of durable goods can be particularly affected by the uncertainty, we find that the measures of output in durable industries are significantly negatively affected by oil uncertainty, relative to non-durable industries. We explain our empirical findings in a two-sector macro model in which oil is an essential input for the production of consumption goods. The oil supply from existing wells is subject to exogenous fluctuations, and firms manage oil inventories to mitigate the consequences of oil 3

4 supply shocks. In times of high oil supply volatility, they therefore increase their inventories to alleviate the probability of a stock-out in the event of a large negative supply shock. As a result of this precautionary savings effect, the amount of oil available for production in the general macro sector is reduced, and production, consumption, and investments decrease. This effect especially dominates the usual precautionary savings effect to increase physical capital investments when uncertainty rises, such that consumption and investment jointly decrease in our model when (oil) uncertainty goes up. directly supported in the data. Related Literature. These economic mechanisms are Our paper contributes to several strands of literature. In the literature on the macroeconomic impact of oil price fluctuations (e.g., Rotemberg and Woodford 1996; Finn 2; Kilian 28; Dvir and Rogoff 29), it has long been hypothesized that oil-related uncertainty plays a role in addition to (first-moment) oil supply shocks. 2 hypothesis originally goes back to the theory of irreversible investments (see Bernanke 1983; Pindyck 1991). This Based on the effect that the option to delay investing becomes more valuable when oil uncertainty rises, these papers predict a depressing effect on investments and other macro variables, which is confirmed empirically (Elder and Serletis 21 and Jo 214). Our analysis reveals an alternative propagation channel for oil uncertainty shocks based on precautionary inventory stock-ups, which has received much less attention in the literature. 3 To rationalize this mechanism theoretically, we build on and contribute to a recent literature that analyzes the interactions of the oil sector with the broader macroeconomy within two-sector production models (Casassus, Collin-Dufresne, and Routledge 29; 2 See Kilian (214) for an overview. 3 While the important role of inventories is well recognized for commodity markets and for oil in particular (see the classical theory of storage literature developed by Kaldor 1939, Working 1948, Working 1949, Telser 1958, and more modern approaches such as Williams and Wright 1991, Deaton and Laroque 1992, Routledge, Seppi, and Spatt 2, Gorton, Hayashi, and Rouwenhorst 212), the link of precautionary inventory stockups to macroeconomic variables has not been entertained, to our best knowledge. 4

5 Ready 214; Hitzemann 216). Our paper is the first to investigate the effect of oil-related supply uncertainty shocks in such general equilibrium type of model. Second, we contribute more broadly to a macroeconomic literature that identifies uncertainty shocks as a main driver of macroeconomic variables and a source of business cycle fluctuations (e.g., Bloom et al. 214; Christiano, Motto, and Rostagno 214). A main challenge to general equilibrium models in this literature is to reproduce the empirically observed co-movement of investment and consumption on impact of an uncertainty shock (e.g., Arellano, Bai, and Kehoe 212; Gilchrist, Sim, and Zakrajsek 214; Bloom et al. 214). 4 Due to the resource constraint, consumption has to go up when investment falls, and vice versa (see also Bloom 214). The literature proposes different mechanisms to address this issue, such as price and wage rigidities (Christiano, Motto, and Rostagno 214) or capital flight for the case of small open economies (Fernandez-Villaverde, Guerrón-Quintana, Rubio-Ramirez, and Uribe 211). We add to this literature by proposing an additional channel based on oil inventories. As we show in this paper, oil uncertainty shocks lead to a stocking up of oil inventories, which negatively affects production, consumption, and investment in the general macroeconomy due to the reduced effective oil supply to the market. Finally, our paper adds to the literature on asset pricing in general equilibrium production models (Cochrane 1991, 1996; Rouwenhorst 1995; Jermann 1998; Boldrin, Christiano, and Fisher 21). Related to the modeling difficulties in pure macro models described before, these models typically fail to reproduce a fall in asset prices when uncertainty increases (see Croce 214; Liu and Miao 215, for example), which is established empirically (e.g., Bansal, Kiku, Shaliastovich, and Yaron 214) and critical to generating important features of market risk premia (Bansal and Yaron 24). In particular, the standard choice of convex 4 Empirically, uncertainty shocks typically lead to a drop of both investment and consumption in the short run. Some papers emphasize that in the long run, a rise in uncertainty might actually have a positive effect as a result of growth options (see Gilchrist and Williams 25; Jones, Manuelli, Siu, and Stacchetti 25; Kung and Schmid 214). 5

6 capital adjustment costs in this literature leads to an increased accumulation of capital in response to uncertainty shocks, raising the price of capital with the result of positive equity returns. In our two-sector model, an increase in (oil supply) uncertainty leads to a stocking up of oil inventories instead, and general investment as well as aggregate equity prices fall. Additionally, we relate to the cross-sectional production-based asset pricing literature (e.g., Gomes, Kogan, and Zhang 23; Gomes, Kogan, and Yogo 29) by exploring the effect on industry returns. 2 Empirical Motivation In this section we present our key empirical findings that an increase in oil price volatility has an adverse effect on aggregate real growth. Through a negative cash flow effect, it has a negative impact on asset prices, especially in durable-good producing industries that are sensitive to oil as an input factor. We also show that a rise in oil volatility lowers consumption of oil and increases oil inventories, while it does not significantly affect aggregate productivity or oil production. These results motivate our economic model specification in which the ability of firms to stock up, rather than consume, oil in high volatility times leads to a negative impact of oil volatility on aggregate growth and asset valuations. 2.1 Data In our empirical analysis we use macroeconomic data related to production and consumption in the aggregate economy and the oil sector, equity price data, and option price data for the market index and oil. All the macroeconomic data are real and seasonally adjusted. Due to the availability of the option data, our benchmark sample runs quarterly from 199Q1 to 214Q1. 6

7 Our aggregate macroeconomic data are for the United States, and include consumption, comprised of expenditures on nondurable goods and services, GDP, private domestic investment, and employment. The data come from the Bureau of Economic Analysis (BEA). We additionally collect the Total Factor Productivity (TFP) index data which correspond to the estimates of the Solow residual for the US economy. For robustness, we also consider the utilization-adjusted productivity measure proposed by Basu, Fernald, and Kimball (26). The oil quantity data come from the U.S. Energy Information Administration. 5 Our oil supply measure corresponds to the world production of crude oil. To measure oil usage and inventories, we use total consumption of petroleum products and total petroleum stocks, respectively. The long sample of oil consumption and stock data is only available for the OECD countries. For robustness, we also check the results using the oil consumption and inventories in the United States. In terms of the asset price data, we use crude oil futures data to construct excess returns on oil. These data are obtained from the Commodity Research Bureau (CRB). The return data for a broad market portfolio comes from CRSP. We further collect return and income data for equity portfolios. Following Gomes, Kogan, and Yogo (29), we use the benchmark input-output accounts table in the BEA to identify industries whose final demand has highest value-added to personal consumption expenditures on durable goods, non-durable goods and services. Similar to Eraker, Shaliastovich, and Wang (215), we aggregate non-durables and services into a single value-weighted non-durable portfolio. 6 In addition, we follow Chiang, Hughen, and Sagi (215) to construct a value-weighted oil producer portfolio. An important object for our analysis is the amount of uncertainty in financial and macroeconomic data. Our benchmark uncertainty measures are constructed using the option data on equity and oil prices. Specifically, we use the volatility index VIX, constructed from the 5 The data are available at 6 Our results are similar when using only the non-durable-good producing firms in the portfolio. 7

8 cross-section of S&P 5 index option prices as the model-free estimate of the aggregate market volatility. In a similar fashion, we construct the option-implied oil volatility measure to capture the ex-ante uncertainty in the oil markets. For robustness, we consider several alternative uncertainty measures. First, we construct realized, rather than ex-ante, uncertainty using the high-frequency return data. That is, we use squared daily equity and oil returns over the quarter to obtain realized variation measures in equity and oil markets, respectively. We further consider other measures of aggregate uncertainty, such as the Baker, Bloom, and Davis (213) economic policy uncertainty index available at the Fred, and the stochastic volatilities of real consumption growth, constructed from an AR(1)-GARCH(1,1) filter to the real consumption growth data. The key summary statistics for the data are reported in Table 1. In our sample, the real aggregate growth rates average between 1 and 2%. The volatilities of the standard aggregate production and consumption series are about 1%, with the exception of real investment whose volatility is 7%. The oil-related measures are about twice more volatile than the consumption and output growth in the United States. Most of the macroeconomic variables are mildly persistent, except for the oil-related measures for which the autocorrelation coefficients are close to zero or even negative. In terms of the asset-price moments, the equity risk premium is about 6% in our sample, while the average excess oil return is 4%. The volatility of oil return is almost 4%, which is twice as high as the volatility of the equity return. The implied oil volatility is also larger than the implied equity volatility, and is twice as volatile. We show the time series of returns and volatilities in equity and oil markets in Figure 1. Both oil and equity returns are quite volatile and further, the amount of conditional volatility varies persistently in the sample. As shown in Table 2, volatilities in oil and equity markets are quite correlated: the correlation coefficient is about 6% in the benchmark sample, though, it drops to 5% excluding the Financial Crisis. In equity markets, the two largest spikes in volatility correspond to the stock market crash in November of 1987, and the Great Recession 8

9 at the end of 28. The equity volatility is also elevated in the LTCM crisis of 1998, and the dotcom crash in 22. All of the turbulent equity market periods are associated with a significant decline in equity prices. In oil markets, oil volatility exhibits larger level and variation, relative to equity volatility. Also, a rise in oil volatility can be associated with both sharp increases in the underlying prices, as in the Gulf War of 199, as well as decreases in oil prices, as in the Great Recession in 28. Oil volatility is also high in 1986 due to the oil price collapse caused by the decision of Saudi Arabia and several of its neighbors to increase its share in the oil markets. 2.2 Oil Volatility and Current Growth We start our analysis by considering contemporaneous correlations of volatility with aggregate macroeconomic variables. The first panel of Table 2 shows our evidence for the benchmark sample from 199 to 214, and the bottom panel shows the robustness to Financial Crisis period which features abnormally large movements in the volatility. The Table shows that all the considered measures of economic growth, such as consumption, GDP, investment, dividend, and employment growth, decline significantly at times of high oil volatility. For example, the correlation between GDP growth and oil implied volatility is -.55, and it is -.49 for investment growth and -.55 for change in employment. The economic growth rates also decline at times of high equity volatility. However, the growth rate correlations with equity volatility are all smaller, in absolute value, compared to those with oil volatility. For example, for a benchmark sample, the correlation of GDP growth with oil volatility is -.55, relative to -.4 for equity volatility, and the magnitudes are -.49 and -.37, respectively, for investment growth, and -.55 and -.49 for employment growth. The evidence is quite similar excluding the Great Depression period, as shown in the 9

10 bottom panel, and in the longer sample which uses realized variances to compute oil and market uncertainties (see Appendix Table A.1). Next we consider the covariation of volatility with oil-related quantity data. Oil consumption declines when oil volatility is high: the contemporaneous correlation is -.36 both in the benchmark sample and excluding the crisis. The correlations are much weaker for equity volatility. Indeed, the correlation between oil consumption growth and equity implied volatility is in fact zero outside the Financial crisis. In our benchmark sample, oil stock goes up at times of high oil volatility, however, these correlations are rather weak. To the extent that there are delays in adjusting oil stock in real world, we expect the oil stock to increase in the future, rather than contemporaneously. We show the evidence for that later in the predictability results. We further examine the link between the volatility and the productivity measures in aggregate and oil sectors. In our model, the TFP and oil production growth are the exogenous processes which drive the economy, so it is important to establish how much of oil volatility effect exists at the level of the economic primitives. Table 2 shows that the TFP growth rates are negatively correlated with oil volatility. However, these correlations are weaker relative to other macroeconomic variables. For example, excluding the Financial Crisis, the correlation of oil volatility with TFP are about twice lower, in absolute value, relative to the correlations of oil volatility with consumption, output, investment, and employment. Similarly, the correlation of oil supply growth with volatility is two to three times weaker than the correlation of oil consumption growth with volatility. This suggests that the effect of oil volatility on endogenous macroeconomic variables is larger than that on the exogenous driving processes. We show further evidence for that in the predictive regressions. Finally, we show the evidence for the co-movements of the aggregate variables with oil return itself. Oil return is weakly procyclical, however, the correlations of oil returns with standard 1

11 macroeconomic variables are nearly zero outside the Financial Crisis. Oil prices have more substantial correlations with oil-related quantities. In the data, growth rates in oil production and oil stock contemporaneously decline at times of high oil prices, while oil consumption increases. Our key results are based on the benchmark sample from 199 to 214, given the availability of the option data. To show the robustness of our results, we also consider a longer sample starting from 1983, for which we can use realized volatility measures computed from the daily oil and equity returns. As shown in Table A.1, the results for the sample are similar to our benchmark findings. These findings suggest an important link between oil volatility and economic growth rates, relative to equity volatility. Next we formally examine the information in the two volatility measures for the expected future growth rates. 2.3 Oil Volatility and Future Growth To show the distinct information in oil variance for future economic growth, we consider a predictive regression setup: 1 h h y t+j = a h + b hx t + error, j=1 where y is the macroeconomic variable of interest, and x t is the set of predictors. In the benchmark specification, the predictors include the lag of the predictive variable itself, oil variance, equity variance, and oil return. The regressions are done on quarterly frequency from 199 to 214. When h = we consider a contemporaneous relation between y t and the set of the predictors; for h > it corresponds to the predictive relation h quarters ahead. We consider multiple robustness checks to make sure our results are not sensitive to 11

12 the sample, inclusion of the Financial Crisis, adding asset-price predictors, and alternative measurements of the aggregate volatility. Table 3 summarizes the predictability evidence for future growth in consumption, GDP, investment, employment, and the TFP. For the first four macroeconomic variables, the signs of the loadings on oil variance are negative across all the horizons. That is, controlling for equity variance, oil return, and lag of the variable, a rise in oil variance forecasts a decline in future aggregate growth 1 to 4 quarters ahead. All slope coefficients on oil variance are statistically significant at 1 quarter horizon, while the significance drops with the horizon. 7 The Tables further shows that the signs of the equity variance loadings tend to be negative as well. However, across all the horizons the estimates of the impact of equity variance are never significantly different from zero. In terms of the effect of oil prices, the signs of the coefficients are negative for consumption and GDP growth, positive for employment, and the evidence is mixed for future investment growth. The R 2 in these predictability regressions is quite high, and varies from about 2% for future GDP and investment, to about 4% for future consumption, and 7-8% for future employment. Oil variance also predicts a decline in the TFP initially, but after 2 quarters the signs on oil variance turn positive. All of the coefficients in the TFP regressions are insignificantly different from zero. The coefficients on equity variance are positive, and also insignificant. Finally, the R 2 s in these regressions are below 1%. Overall, consistent with our contemporaneous correlation evidence in Table 2, the data do not feature a strong link between aggregate TFP and oil volatility. To quantify a relative impact of variance on aggregate variables, in Figure 2 we show the impulse responses of future consumption, output, investment, and employment to one-standard deviation shock in oil and equity variance. The impulse responses are based on a VAR(1) 7 The responses are magnified and the statistical significance improves in the period which excludes very volatile observations of the Financial Crisis, as shown in Table A.4. 12

13 specification fitted to the observed equity variance, oil variance, oil returns, and the macroeconomic variables of interest, over the benchmark sample from 199 to 214. To compute the impulse responses, we always put the macroeconomic variable last, and put the oil return before the oil variance. We then consider two orderings for the oil and equity variance. In the first, conservative case, we put the equity variance first, so that the shock in equity variance affects future oil variance. We also consider an alternative ordering in which oil volatility comes before equity volatility. The Figure shows that under the first scenario in which oil variance responds to equity variance shocks, the two variances have a very similar negative impact on future economic growth rates. Consumption growth declines by about.3%, annualized, following the shock, and declines further one quarter after the shock. Output and investment drop by.66% and 2.75%, respectively, and employment growth tends to decline for several quarters after the shock. When we change the ordering and let oil variance lead equity variance, we find that the impact of oil variance significantly increases, while the role of equity variance diminishes by more than a half. At its peak, the impact of oil variance is to drop consumption growth by.55%, output by.85%, investment by 4.25%, and employment by.65%. The impact of equity variance is several times smaller. Table 4 shows the predictability evidence for the role of oil uncertainty for production and consumption of oil. The sign predictive coefficient for oil production is initially negative, but it turns positive after 3 quarters. All of the coefficients are insignificantly different from zero. The R 2 s in these regressions are all below 1%. While the data do not indicate a strong relation between oil production and oil volatility, future oil consumption tends to drop, while future oil inventories increase following an increase in oil variance. Indeed, Table 4 shows that oil variance has negative and significant effect on oil consumption 1 quarter ahead, and a positive and significant effect for next-quarter oil stock. To gauge quantitative impact of oil variance, we consider the impulse responses of future oil consumption and oil inventory to oil volatility shocks in Figure 3. We compute the impulse 13

14 responses from a VAR(1) fitted to oil supply growth, oil return, oil volatility, oil inventory, and oil consumption growth data, in that order. The Figure shows that oil inventories increase by.5% one quarter after the impact, while oil consumption declines by about.6%. We consider multiple alternative specifications to check the robustness of our results, such as using a longer sample from 1983 and relying on realized variance measures to capture movements in uncertainty (Tables A.2 - A.3), excluding the Financial Crisis (Tables A.4 - A.5), and adding additional asset-price controls, such as the market price-dividend ratio, short rate, and the term spread (Tables A.6 - A.7). We also replace market variance by alternative measures of aggregate uncertainty, such as the Baker-Bloom-Davis economic policy uncertainty index (Table 5), and the conditional variance of the output growth (Table 6). The results are quantitatively very similar to the benchmark findings. 2.4 Oil Volatility and Asset Prices The correlation evidence in Table 2 suggests that equity returns drop at times of high oil variance. Indeed, the correlation of equity returns with oil implied variance is -.3 in the benchmark sample, and about -.15 excluding the crisis. Impulse responses in Figure 4 quantify the dynamic impact of oil volatility on equity prices. The figure shows that independent of the relative ordering of equity and oil volatility, oil volatility has a negative effect on market valuations. Oil returns, on the other hand, have a much weaker relation with oil variance. Excluding the crisis, the correlation of oil returns with oil implied variance is positive and equal to.3. This is consistent with our earlier discussion that an increase in the underlying oil variance can be caused both by large positive and negative shocks to oil prices. 14

15 We further find that the effect of oil volatility on asset valuation varies considerably across industries. In particular, we construct durable and non-durable equity portfolios and oil producer portfolio, following Gomes, Kogan, and Yogo (29) and Chiang, Hughen, and Sagi (215), respectively. We regress industry returns on the market return, oil return, and the equity and oil implied volatilities, which allows us to estimate the sensitivity of the industry portfolios to these factors. Table 7 shows that the durable portfolio exhibits the largest exposure to oil uncertainty, with a negative and statistically significant beta of On the contrary, the impact of oil uncertainty on the non-durables and oil producers portfolio is small in magnitude, positive and statistically insignificant. 8 Using an alternative sorting based on 3 Fama-French industries, we find that the largest negative effect of oil uncertainty is concentrated in the Auto sector, for which the oil variance exposure is -.7, while Chemicals and Oil portfolios have positive exposures. The asset prices can be driven by the discount rates or the cash-flow shocks. In our sample, we do not find a significant link between the risk premia and oil variance. This is consistent with Christoffersen and Pan (214), who show that the implied oil volatility does not have a predictive power for equity returns in a long sample, but only in the financialization period starting in 24. On the other hand, we find that oil volatility has a significant impact on the output measures across sectors, consistent with our earlier evidence for the aggregate macro series. Table 8 shows the results using the industrial production index for the aggregate economy, durable and non-durable consumer good sectors, auto sector, and crude oil mining. While the oil volatility negatively impacts current and future aggregate production, its effect more than doubles for the durable consumer good sector, and is especially large for the manufacturers of motor vehicles. For example, 1 quarter ahead slope coefficients increase, in absolute value, from -.1 for the aggregate series to -.4 and -.82 for durables and autos, respectively. Interestingly, nondurable consumer and oil mining sectors do not 8 These findings are robust to excluding the Financial Crisis, as shown in the bottom panel, or starting a sample in 1983 (see Table A.8). 15

16 significantly respond to oil volatility, as all the slope coefficients are essentially zero. We obtain very similar results using earnings data for durable and non-durable industries and the oil producers (see Table 9). Our portfolio evidence is consistent with the hypothesis in Bernanke (1983) and the empirical evidence in Elder and Serletis (21) that oil price uncertainty has a more significant effect on the aggregate consumption of durable goods. The heterogeneity in cash flow exposures to oil volatility also helps explain a much more pronounced negative impact of oil uncertainty on asset prices in the durable sector and autos relative to non-durable sector and the aggregate economy. In the next section we provide some intuition for this empirical evidence based on a differential sensitivity of durables and non-durables industries to oil as an input factor. 3 Model We explain our empirical findings within a macro model in the style of Ready (214) and Hitzemann (216), featuring an oil sector and a general macro sector. As the main novel ingredient, we introduce stochastic uncertainty of the oil supply into the model. Shocks to oil supply uncertainty endogenously translate to changes in oil price volatility, motivating the use of the price-based oil uncertainty measure in our empirical analysis. We show that in line with a precautionary savings motive, oil producers stock up their inventories when oil supply uncertainty increases and sell less oil to the market. The decrease in effective oil supply translates to the macro sector and depresses output, consumption, and investment. 16

17 3.1 Setup Final goods producer The representative firm in our model produces a final good Y t = (A t N t ) 1 α Z α t (3.1) with the input of labor N t and an intermediate good Z t, where the total factor productivity is denoted by A t. Production of the intermediate good requires general capital K t and oil J t as an input. More specifically, the intermediate good is a CES aggregate of these two input factors, Z t = [(1 ι)k 1 1 o t + ιj 1 1 o t ] o, (3.2) where ι = ι o describes the oil share and o is the constant elasticity of substitution. The oil input of the firm is purchased from oil producers as described below. On the other hand, the firm maintains a general capital stock K t in line with the classical real business cycle framework. Accordingly, the capital accumulation equation is given by K t+1 = (1 δ)k t + I t G t K t, (3.3) where I t is physical capital investment and G t is an adjustment cost function G t (I t /K t ) = I t /K t (a + a (I t /K t ) 1 1 ξ ) (3.4) ξ as proposed by Jermann (1998). The firm generates revenues by selling the part of the final output that is not invested again to the households, creating a cash-flow of Y t I t. On the other hand, the oil input J t is purchased from the oil producer at price P t, and workers are paid wages W N t for their hours 17

18 worked N t. Overall, the final goods producer maximizes the expected sum of discounted cash-flows E t s= M t+s (Y t+s I t+s P t+s J t+s W N t+sn t+s ), (3.5) where M t+s is the s-period stochastic discount factor at time t. Oil Producer The oil sector is represented by an oil producing firm which is endowed with an amount of oil wells containing U t = A t U (3.6) barrels of oil below ground. To ensure balanced growth, we assume that the oil wells grow with the general macroeconomy at A t. This is in line with a model where firms endogenously invest a certain amount of their output Y t to drill new oil wells (see Hitzemann 216). Keeping the model as simple as possible, we do not explicitly consider the oil drilling decision in here and take the amount of oil wells as exogenous. Accordingly, the amount of below-ground oil in existing wells is also not reduced by oil extraction in this model. The production of oil takes place at a stochastic extraction rate κ t, such that E t = κ t U t (3.7) barrels of oil are extracted and added to the producer s above-ground inventories. The oil inventories are actively managed and evolve as S t+1 = (1 ω)s t Π t A t + E t+1 D t+1. (3.8) 18

19 Accordingly, the oil producer decides at each point in time how much oil D t to sell to the firms for production and how much to store above ground at an inventory cost of ω. An important restriction is that inventories cannot become negative, which gives rise to a precautionary savings motive that is at the center of the economic mechanism studied in this paper. Technically, we approximate the non-negativity condition by a smooth stock-out cost function Π t (S t /A t ) = π 2 (S t/a t ) 2, (3.9) as proposed by Hitzemann (216). Given these ingredients, the oil producer maximizes the expected discounted cash-flows from oil sales to the final goods producing firm, which are given by E t s= M t+s P t+s D t+s. (3.1) Macro and Oil Productivity Risk In our model, both the general macro sector and the oil sector are subject to productivity risk. We specify the productivity of the macro sector in line with Croce (214), i.e., A t+1 = A t exp{µ + x t + e wt ε A t+1}, (3.11) x t+1 = φx t + e w t+1 ε x t+1, (3.12) w t+1 = ρ w w t + ε w t+1. (3.13) Here ε A t N(, σa 2 ) are short-run shocks to macroeconomic productivity growth while ε x t N(, σ 2 x) are persistent (long-run) shocks to productivity growth. In addition, we also consider uncertainty shocks ε w t N(, σ 2 w) to macro productivity. 19

20 The productivity risk in the oil sector stems from fluctuations in the extraction rate from existing oil wells given by κ t+1 = η(1 χ) + χκ t + e vt ηε κ t+1, (3.14) v t+1 = ρ v v t + ε v t+1. (3.15) In addition to the level shocks ε κ t N(, σκ), 2 we introduce oil-specific supply uncertainty shocks ε v t N(, σv) 2 into the model. As oil supply uncertainty shocks endogenously translate to changes of oil price volatility in our model, we identify the impact of these shocks with the effects of fluctuating oil price volatility documented in our empirical analysis. All shocks considered in our model are i.i.d. and mutually independent. Household The representative household consumes a CES bundle of the final consumption good C t and leisure L t, given by C t = [τc 1 1 ξ L t + (1 τ)(a t 1 L t ) 1 1 ξ L ] ξ L, (3.16) and maximizes Epstein and Zin (1991) utility V t = [ (1 β) C 1 1 ψ t ] [ ] ψ 1 ψ 1 + βe t V 1 γ 1 γ t+1 (3.17) with risk aversion γ and an intertemporal elasticity of substitution ψ. The utility maximization is subject to the standard wealth constraint W t+1 = (W t C t + W N t N t )R W t+1 (3.18) 2

21 and the labor supply constraint N t + L t = 1. (3.19) 3.2 Equilibrium To calculate the model s equilibrium, we derive the firms and the household s first order conditions. 9 As a result, we obtain, first, the intratemporal conditions for the oil price P t = Q S t Y t = Y t = α ι J t J 1 o t Z 1 1 o t (3.2) and for labor wages W N t = C L t / C C t = (1 α) Y t N t. (3.21) Second, the intertemporal Euler condition E t [M t+1 R t+1 ] = 1 (3.22) holds for the returns of all assets traded in the economy, with the pricing kernel given by M t+1 = β ( ) 1 Ct+1 C t ξ L ( Ct+1 C t ) 1 1 ξ L ψ V t+1 E t [ V 1 γ t+1 ] 1 1 γ 1 ψ γ. (3.23) The Euler equation especially applies to the return of investment in the general macro sector R I t+1 = α(1 ι) Y t+1 K o 1 t+1 Z 1 o 1 t+1 I + ((1 δ) + G t+1 t+1 K t+1 G t+1 )Q I t+1, (3.24) Q I t 9 The household s first order conditions are the same as in an endowment economy with the same consumption goods. For the derivation of the firms first order conditions, see Appendix A.1. 21

22 with Q I t = 1, and the return on oil inventories 1 G t Rt+1 S = (1 ω Π t)q S t+1. (3.25) Q S t With these expressions, we can define the equity market return as the weighted average of R I and R S, Rt+1 M = K tq I t Rt+1 I + S t Q S t Rt+1 S. (3.26) K t Q I t + S t Q S t Given the risk-free rate R f t = 1 E t [M t+1 ], (3.27) we calculate the equity risk premium as R LEV ex,t = (1 + DE)(R M t R f t 1) (3.28) and account for financial leverage by assuming an average debt-to-equity ratio DE of 1 (see, e.g., Croce 214). Having the first order conditions as well as the market clearing conditions, C t + I t = Y t and D t = J t, we can reformulate the model as a central planner s problem according to the welfare theorems. We solve this problem numerically by a third-order approximation using perturbation methods as provided by the dynare++ package. 3.3 Calibration Table 1 shows the parameters of the calibrated model. Following the literature on longrun risk in consumption- and production-based asset pricing (Bansal and Yaron 24; Croce 214), we set the relative risk aversion γ to 1 and the intertemporal elasticity of substitution ψ to 2, such that households in our model have a preference for the early resolution of 22

23 uncertainty. We set the subjective discount factor β to.97. The parameters α, δ, µ, τ, σ A, φ, σ x, ρ w, and σ w describing the macro sector are chosen in line with Croce (214). We set the constant elasticity of substitution ξ L between leisure and consumption to.9. For the oil sector, we fix the oil inventory cost ω as well as the mean η and the mean-reversion χ of the oil production rate according to the benchmark calibration of Hitzemann (216). We calibrate the adjustment cost parameter of the macro sector ξ to match the volatility of general consumption relative to output, and the oil inventory stock-out cost parameter π to the level of oil inventories relative to yearly oil production (see the first panel of Table 11). The elasticity of substitution o of oil as a production input is set to.225 in line with Ready (214), and we calibrate the oil share ι to match the ratio of oil input relative to general consumption. Finally, we match the oil price volatility s level, mean-reversion, and volatility by calibrating the corresponding parameters of the oil supply process σ k, ρ v, and σ v. This way, we especially ensure that a one standard deviation shock to oil price volatility as considered in the empirical section corresponds to a one standard deviation shock to oil supply volatility in the model. The second panel of Table 11 reports price and quantity moments that the model is not explicitly calibrated to. Overall, we see that all important moments are in a reasonable order of magnitude, and deviations are in line with the model without an oil sector as proposed by Croce (214). 3.4 Inspecting the Mechanism Our model provides insights into the economic mechanism behind our main empirical finding that an increase of uncertainty in the oil sector depresses macroeconomic growth. The mechanism is illustrated by the impulse response functions for an oil supply uncertainty shock based on our model, as presented by Figure 5. We see that a rise in uncertainty 23

24 regarding oil supply prompts the oil producer to stock up above-ground oil inventories. The reason is that a positive shock to oil supply uncertainty makes large negative and positive oil supply (level) shocks more likely. To be able to cushion a large negative oil supply shock and to smooth oil consumption over time, oil producers need to increase their inventories to alleviate the probability of a stock-out. As a result of this precautionary savings effect, the oil producer curbs the amount of oil that is sold to the market. As oil is an important input factor for the production of goods in the general macro sector, the reduced oil supply negatively affects the output of the final consumption and investment good. Therefore, the precautionary savings effect in the oil sector spills over to the general macroeconomy. In consequence of the declining output, the investment and consumption of the general good also decreases. The magnitude of the effect of oil supply uncertainty shocks on the macro sector strongly depends on the substitutability of oil, as specified by the CES parameter o. This becomes obvious when we vary the value of o, as shown by Figure 6. In the case of a lower o, the impact on the macro sector is clearly more pronounced than in the benchmark calibration, while it is the other way round for a higher o. On the quantitative side, a one standard deviation increase of oil supply uncertainty in the model leads to a rise in oil inventories by almost 1%, reducing the effective oil supply to the market by more than.5%. In the macro sector, this yields a decrease in output by.5%, a fall in consumption by.4%, and investments declining by more than.7%. These effects on the macroeconomy are overall roughly in a similar order of magnitude as the ones observed in the data. 3.5 Effect on Oil Prices and Equity Returns The model also explains the behavior of oil prices and equity in response to oil uncertainty shocks. Figure 5 shows that oil prices increase in response to a rise in oil supply volatility. 24

25 The reason is that oil becomes effectively more scarce for the market when agents have a strong incentive to stock up their inventories. In this sense, our model rationalizes the notion of precautionary demand shocks for oil, which Kilian (29) finds to be an important driver of oil prices. Figure 5 also illustrates the effect of oil volatility fluctuations on equity returns. As a result of the depressing effect on output, consumption, and investment, there is also a clear negative influence on aggregate equity returns, in line with what we see in the data. Considering the cross-section of different industries reveals that this negative effect is clearly present in the returns of the final goods producing macro sector, rt I (see also Figure 6), but not for the return of oil firms, rt S. The oil firm s return is actually positive, in line with higher revenues for oil producers due to the increasing oil price. This intuition explains why the response of aggregate equity to increasing oil uncertainty is clearly negative in the data, but there is no such effect (or even a positive one) for oil producing industries. Furthermore, an important result of our empirical analysis is that the negative aggregate equity return is primarily driven by durable goods producers, as opposed to non-durables producing firms. The differential behavior of durables and non-durables industries in more general is highlighted by the existing asset pricing literature and rationalized in the context of general equilibrium models (see Yogo 26; Gomes, Kogan, and Yogo 29). When it comes to energy consumption, a special property of several durables is that they require additional energy input to be used, as for example cars or appliances. One could capture this particularity by having oil as part of the household s consumption bundle, as in Ready (214) or Hitzemann (216). We refrain from such an extension of our model for the sake of simplicity, and think of durables instead in an ad-hoc way as goods which are very sensitive to oil as an input factor (low o), while oil can be substituted more easily for non-durables (higher o). As Figure 6 25

26 illustrates, the negative response of aggregate equity returns is much more pronounced for the low o case. In this sense, the model provides a first intuition for the differential effect of oil uncertainty shocks on durables and non-durables industries. 4 Conclusion We show novel empirical evidence that oil price variance captures significant information about economic growth and asset prices. An increase in oil variance predicts a decline in current and future growth rates of consumption, output, investment, and employment 1 to 4 quarters ahead, controlling for current growth rate in the corresponding variables, current oil returns, and the market variance. We further show that the market equity price drops at times of high oil uncertainty, while oil prices themselves have only a weak relation to oil uncertainty which turns positive outside the Financial Crisis. We provide a two-sector macro model to explain these empirical findings. In the model, firms manage oil inventories to mitigate the consequences of oil supply shocks. In times of high oil supply volatility, they increase their inventories to alleviate the probability of a stock-out. As a result of this precautionary savings effect, the amount of oil available for production in the general macro sector is reduced, and production, consumption, and investments decrease. This effect dominates the usual precautionary savings effect to increase physical capital investments when uncertainty increases, such that consumption and investment jointly decrease in our model when (oil) uncertainty rises. These economic mechanisms are directly supported in the data. 26

27 A Appendix A.1 Firms First Order Conditions Final goods producer Without loss of generality, consider (3.5) at time and add the Lagrange multiplier Q I t for the resource constraint (3.3): max I t,k t+1,n t,j t E t= M t (Y t I t P t J t Wt N N t Q I t (K t+1 (1 δ)k t I t + G t K t )). (A.1) Setting the derivative with respect to I t to zero yields Q I t = 1. (A.2) 1 G t Setting the derivative with respect to K t+1 to zero, we obtain E t α(1 ι) M t+1 Y t+1 K o 1 t+1 Z 1 o 1 t+1 I + ((1 δ) + G t+1 t+1 K t+1 G t+1 )Q I t+1 = 1. Q I t (A.3) Setting the derivative with respect to N t to zero, we have W N t = Y t N t = (1 α) Y t N t. (A.4) 27

28 Finally, we set the derivative with respect to J t to zero and get Y t P t = Y t = αι. (A.5) J t J 1 o t Z 1 1 o t Oil Producer Without loss of generality, consider (3.1) at time and add the Lagrange multiplier Q S t for the resource constraint (3.8) max D t,s t E M t (P t D t Q S t (S t (1 ω)s t 1 + Π t 1 A t 1 E t + D t )). t= (A.6) Setting the derivative with respect to D t to zero, we get P t = Q S t. (A.7) Setting the derivative with respect to S t to zero yields [ ] (1 ω Π E t M t)q S t+1 t+1 = 1. (A.8) Q S t A.2 Appendix Tables 28

29 Table A.1: Correlation Evidence: Sample Oil RV Equity RV Oil return sample Consumption growth Output growth Investment growth Employment growth TFP growth Excess equity return Excess oil return Equity RV Oil consumption growth Oil production growth Oil stocks growth sample, excluding 26Q3-28Q4 Consumption growth Output growth Investment growth Employment growth TFP growth Excess equity return Excess oil return Equity RV Oil consumption growth Oil production growth Oil stocks growth The table reports correlations between volatility measures, oil returns, and aggregate economic and assetprice variables. The realized oil and equity variances are constructed from the oil and equity realized returns, respectively. The top panel uses quarterly data from 1983 to 214, and the bottom panel excludes 26Q3-28Q4 episode. 29